Greene was born in Brooklyn, New York. Her mother is a guidance counselor, and her father is a dentist. She attended W. Tresper Clarke High School, in Westbury, New York. She spent summers at Cejwin Camps in Port Jervis, New York where she performed in musical theater productions, including the role of Tzeitel in a 1966 production of Fiddler on the Roof. She was first married to Tibor Hardik. She also had a relationship with Martin P. Robinson. She has been married to Christian Klikovits since September 25, 2003.

Greene’s career began as a nightclub singer in clubs such as The Brothers and Sisters, Grand Finale and Reno Sweeney. She received rave reviews from critics such as Rex Reed, George Bell and John S. Wilson. Around this time she befriended the late Peter Allen. Her first starring role was as the lead in the notorious Broadway bomb, Rachael Lily Rosenbloom (And Don't You Ever Forget It) in 1973, which co-starred Anita Morris.

She then won the starring role of Chrissy in Joseph Papp's production of In the Boom Boom Room. Her reviews brought her to the attention of Paul Mazursky who was at that time casting for Next Stop, Greenwich Village; she got the role of Sarah, her first starring role in a film. Continuing her work with Papp's New York Shakespeare Festival, Greene next essayed the role of Jenny in The Three Penny Opera at the Vivian Beaumont Theatre in Lincoln Center for which her performance was nominated for a Tony Award.

In addition to a number of other productions with the New York Shakespeare Festival as well as numerous other companies, Greene formed a close working relationship with the WPA Theatre, where she met Howard Ashman and Alan Menken, which led to a close, long-lasting friendship. This led, in turn, among other productions, to the role for which she is perhaps most-widely known, that of the hapless Audrey in Little Shop of Horrors, a role she reprised in the film version opposite Rick Moranis.

Greene has worked extensively in theater, such as the part of Suzanne/The Little Rose in The Little Prince and the Aviator, as well as in films such as I'm Dancing as Fast as I Can, Léon, Talk Radio, and Pump Up the Volume. She has appeared on television in Miami Vice, Glory! Glory!, The Adventures of Pete and Pete, Cybill, Law & Order, Suddenly Susan, The X-Files, Mystery Woman: Sing Me a Murder, Fielder’s Choice and Heroes. In 1983 she was the voice of Creeping Ivy in the animated TV special The Magic of Herself the Elf.

Greene released an album in 2004 entitled In His Eyes, on which she was accompanied by her husband and musical director, Christian Klikovits. Her latest work includes the recurring role of Vivian Charles in the television series Pushing Daisies and the voice of Dolly Gopher in the animated Out of Jimmy's Head. Greene was also the voice of Goldie in the Don Bluth film, Rock-A-Doodle.

In the summer of 2009, Greene starred as Miss Adelaide in a concert version of the Broadway musical Guys and Dolls, which had a 3-day engagement at the Hollywood Bowl in Los Angeles, California. Her co-stars included Scott Bakula as Nathan Detroit, theatre veteran and Tony Award winner Brian Stokes Mitchell as Sky Masterson, and Jessica Biel as Sarah Brown. In 2011, she appeared in five episodes of the soap opera The Young and the Restless as Primrose DeVille.

Greene performed in the musical Betwixt! at the Trafalgar Studios in London's West End from 26th July to 20th August 2011.

TRIVIA:

Was nominated for Broadway's 1977 Tony Award as Best Actress (Featured Role - Musical) for a revival of "The Threepenny Opera."

She is most famous as the lispy, bubble-headed blonde Audrey in the stage production of the cult favorite "Little Shop of Horrors," which she played for two years (1982-1984), then transferred to film with the same title _Little Shop of Horrors (1986)_ (qv).

Attended W.T. Clarke High School in Westbury, NY.

Began her career in the early 70's as a cabaret singer in such famed New York City night spots as Reno Sweeney's in Greenwich Village.